They absolutely would have moved around since one of the most common ways to get the apprenticeships was to sign up to help with an army that was mobilizing for war. Militaries needed a lot of blacksmiths to tag along as support and they needed a lot of apprentices for manual labor. When they came back from, they often had a little more choice in where to go back to so they had quite a bit more mobility over all.

Not just that, but "head out with the military, stay where you end up (or somewhere along the route)" is a tried-and-true method of moving people throughout history. How else would you end up with Latin dialects spoken over a range from Portugal to the Black Sea?

> How else would you end up with Latin dialects spoken over a range from Portugal to the Black Sea?

Same way we ended with almost everyone in Ireland speaking English as their main language?

violent conquest, followed by a brutal subjugation and a cultural genocide.

Sure, but also (and corollary to the first three) "leaving people behind in power who speak English".